Correct Answer - C

(c ) `H = (V^(2))/(R ) t`

Since supply voltage is same and equal amount of heat will produce, therefore

`(R_(1))/(t_(1)) = (R_(2))/(t_(2))` or `(R_(1))/(R_(2)) = (t_(1))/(t_(2))`

But `R prop l implies (R_(1))/(R_(2)) = (l_(1))/(l_(2))`

By (i) and (ii), `(l_(1))/(l_(2)) = (t_(1))/(t_(2))`

Now `l_(2) = (2)/(3) l_(1) implies (l_(1))/(l_(2)) = (3)/(2)`

`:.` By equiation (iii), `(3)/(2) = (15)/(t_(2)) implies t_(2) = 10` minutes